Bang-Bang Control Development of Permeability Changes in a Membrane Model

TL;DR

This paper applies control theory, specifically bang-bang control, to model how nerve membranes regulate permeability, providing insights into neural activity regulation and membrane adaptation mechanisms.

Contribution

It introduces a novel bang-bang control policy for membrane permeability regulation based on Lyapunov's stability, linking control theory with neural membrane dynamics.

Findings

Permeability regulation driven by a switching function dependent on membrane potential.

Control policy effectively drives membrane from unstable firing to resting state.

Integration of control theory with Hodgkin-Huxley equations enhances understanding of neural regulation.

Abstract

The application of systems and control theory to membrane physiology is presented here. Modeling efforts have focused on describing those physiologically realistic mechanisms which govern the regulation of membrane permeability in nerve. The motivation behind identifying such mechanisms lies in understanding the morphology of neural activity on a meaningful and analytically tractable level. The suggested merit of integrating control theory into the analysis lies in providing how a membrane effectively adapts to changes in permeability and through what governing mechanisms. The value in producing such an understanding lies in mirroring biological reality in a more formal manner than could be achieved solely through experimental means. A bang-bang control policy describing the permeability correction mechanisms is developed using Liapunov's Stability Criteria. Both changes in membrane potential and kinetic rates are required to implement the policy. The policy describes the inherent mechanisms of the membrane which act to drive its permeability from unstable firing to the resting potential state. It is shown that these permeability changes in state are governed by a switching function that depends on the membrane potential and a dominant controlling parameter. The control policy is discussed in the context of solutions of the Hodgkin-Huxley Equations of Ionic Hypothesis.